Kavli Affiliate: Ran Wang
| First 5 Authors: Mohamed Naveed Gul Mohamed, Suman Chakravorty, Raman Goyal, Ran Wang,
| Summary:
We consider the problem of nonlinear stochastic optimal control. This problem
is thought to be fundamentally intractable owing to Bellman’s "curse of
dimensionality". We present a result that shows that repeatedly solving an
open-loop deterministic problem from the current state with progressively
shorter horizons, similar to Model Predictive Control (MPC), results in a
feedback policy that is $O(epsilon^4)$ near to the true global stochastic
optimal policy, where $epsilon$ is a perturbation parameter modulating the
noise. We also show that the optimal deterministic feedback problem has a
perturbation structure such that higher-order terms of the feedback law do not
affect lower-order terms and that this structure is lost in the optimal
stochastic feedback problem. Consequently, solving the Stochastic Dynamic
Programming problem is highly susceptible to noise, even in low dimensional
problems, and in practice, the MPC-type feedback law offers superior
performance even for high noise levels.
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